Question

4/1•5+4/5•9+4/9•13+...+4/2004•2008=?

Answer 1

Descompunem fractiile , dupa formula (primul termen) =  4/1*5=1/1-1/5  
vom avea:  
1/1-1/5 + 1/5-1/9 + 1/9-1/13 + ... +1/2004-1/2008 = 1/1-1/2008=
      ...........................................................                  =(2008-1}/2008=2007/2008
       acestea doi cate doi se reduc (=0)

Answer 2

[tex]4* [\frac{1}{4} ( \frac{1}{1} - \frac{1}{5} )+\frac{1}{4} ( \frac{1}{5} - \frac{1}{9} )+...+\frac{1}{4} ( \frac{1}{2004} - \frac{1}{2008} )]=\\ = \frac{1}{1} - \frac{1}{5} +\frac{1}{5} - \frac{1}{9} +...+ \frac{1}{2004} - \frac{1}{2008}=\\ =\frac{1}{1} -\frac{1}{2008}= \frac{2007}{2008} [/tex]